In this paper, we introduce the notion of generalized G-β-ψ contractive mappings which is inspired by the concept of α-ψ contractive mappings.
Very recently, Karapınar and Samet [13] introduced the concept of generalized α-ψ contractive mappings, which was inspired by the notion of α-ψ-contractive mappings.
In the present work, we introduce two classes of generalized α-ψ-contractive type mappings of integral type inspired by the report of Karapınar and Samet [7].
In 2006, Isac and Németh [6] gave some fixed point results for nonexpansive nonlinear mappings in Banach spaces inspired by Penot's results where the asymptotically contractiveness was stated in similar terms to condition (1.2).
The implicit midpoint rule (IMR) for nonexpansive mappings in a Hilbert spaceH, inspired by the IMR for ordinary differential equations [6 12], was introduced in [13].
T is M-continuous if it is M-continuous at each x ∈ X. Remark 30 Every continuous mapping is also M-continuous, whatever M. In order to avoid the commutativity condition of the mappings T and g, and inspired by Definition 7, we present the following notion of ( O, M ) -compatibility.
Inspired by [23], we introduce the class of non-self mappings, generalized α-proximal contraction mappings.
In this section, inspired by the notion of ψ S -contractive mappings of [20], we first introduce the notions of generalized ( ψ, f ) λ -expansive mappings and generalized ( ϕ, g, h ) λ -weakly expansive mappings in partial b-metric spaces.
Inspired by the notions of ψ S -contractive mappings of [20], we first introduce the concepts of generalized ( ψ, f ) λ -expansive mappings and generalized ( ϕ, g, h ) λ -weakly expansive mappings.
